dnd-5eshield
Sort of follow on from my previous question.
Shields take an action to don or doff.
In the previous question it was discussed that the reason for this might be needing to strap the shield to your arm/unstrap it.
If your other arm is occupied (caught in a trap, or temporarily turned evil), can you don or doff a shield with just one arm free?
The reason I think you might not be able to is the difficulty of handling the straps with the hand going into the shield.
Anyone can…strap a shield to an arm.
PH, Armor and Shields, p. 144
This jibes with real-world use of the large shields, where the arm provides necessary support to make the shield useful. (Bucklers, or hand shields, may be a different issue, but there are no bucklers in official D&D 5e rules.)
“Manipulating an object” (Mage Hand, PH. p. 256) is different than wielding it.
The hand can only carry 10 pounds. A melee attack can involve thousands of pounds of force — orders of magnitude more than enough to overwhelm the carrying capacity of the hand. Even arrows project much more force than 10 pounds. (And since the hand is not connected to the ground, this force could bat the shield away like a piñata.)
This jibes with the spell description that says Mage Hand “can’t attack.”
Just holding a shield up might convey some benefits to anyone behind it. Depending on the situation, the DM could rule that it provides concealment from view, or some other benefit.
But that’s not wielding a shield.
The description of a Shield in the PHB states...
Shields. A shield is made from wood or metal and is carried in one hand. Wielding a shield increases your Armor Class by 2. You can benefit from only one shield at a time.
Emphasis Mine from PHB p144
Thus, the PHB seems to be referring to shields that are 'held' with the hand, not simply 'strapped' to the arm.
In the medieval era, this was the norm. You'd either have a handle you gripped, a handle + a strap, or two straps (but you'd hold one of them in your fist). If you just strap a shield to your arm and don't have it mechanically affixed to your armor or something...the first time something hits it, it's just going to spin, hit you in the face or legs, and then be useless...because there's nothing holding it in place.
So, the back of your shield probably looks like this
or like this
Best Answer
The rules don't specify; it's up to the DM
As you've noted in your question, the rules specify the time required to don or doff a piece of armor or a shield. However, the rules don't state anything else about what's needed to don or doff armor or shields - specifically, they don't specify whether donning or doffing armor or a shield requires one or both hands to do.
As such, it's up to the DM to decide whether a shield can be donned or doffed with just one hand. For armor, it seems likely that the DM would rule that both hands are needed to put it on or take it off. Shields are a bit more of a gray area, so the DM would ultimately need to make a decision on the matter for themselves.